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Properties

Label 2600.2.fd
Level $2600$
Weight $2$
Character orbit 2600.fd
Rep. character $\chi_{2600}(121,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $848$
Sturm bound $840$

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Defining parameters

Level: \( N \) \(=\) \( 2600 = 2^{3} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2600.fd (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2600, [\chi])\).

Total New Old
Modular forms 3424 848 2576
Cusp forms 3296 848 2448
Eisenstein series 128 0 128

Trace form

\( 848 q + 110 q^{9} - 8 q^{13} + 4 q^{17} - 8 q^{23} + 8 q^{25} + 24 q^{27} + 20 q^{29} - 36 q^{33} - 6 q^{35} - 72 q^{37} + 12 q^{39} - 24 q^{41} - 30 q^{45} + 456 q^{49} + 168 q^{51} - 36 q^{53} - 12 q^{55}+ \cdots - 36 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(2600, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2600, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1300, [\chi])\)\(^{\oplus 2}\)